Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. By analogy with the concept of support vectors original of support vector machines (SVMs), these approaches can be referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the calculation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.